Abstract
There exist many various representations of the space C(X) of continuous functions on a compact space X. Characterizations of this space in the class of real Banach spaces in terms of natural properties of normed spaces were obtained by Arens and Kelley, Jerison, and Myers. In this paper, we give a characterization of C(X) in the class of complex Banach spaces. To this end, we first describe properties of Myers functionals on a complex normed space E and define representations of the orbital function space Cσ(X) with respect to the action of a one-parameter homeomorphism group X. The real and complex cases are considered in parallel.
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